login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A305754 Inverse Euler transform of n^n. 2
1, 3, 23, 223, 2800, 42576, 763220, 15734388, 366715248, 9533817400, 273549419552, 8586984241870, 292755986184548, 10772849583399474, 425587711650564816, 17966217346985801150, 807152054953801845760, 38451365602113352159320, 1936082850634342992601636 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..386

N. J. A. Sloane, Transforms

FORMULA

Product_{k>=1} 1/(1-x^k)^{a(k)} = Sum_{n>=0} (n * x)^n.

a(n) ~ n^n. - Vaclav Kotesovec, Oct 09 2019

EXAMPLE

(1-x)^(-1) * (1-x^2)^(-3) * (1-x^3)^(-23) * (1-x^4)^(-223) * ... = 1 + x + 4*x^2 + 27*x^3 + 256*x^4 + ... .

MATHEMATICA

n = 20; s = {};

For[i = 1, i <= n, i++, AppendTo[s, i*i^i - Sum[s[[d]]*(i-d)^(i-d), {d, i - 1}]]];

Table[Sum[If[Divisible[i, d], MoebiusMu[i/d], 0]*s[[d]], {d, 1, i}]/i, {i, n}] (* Jean-François Alcover, May 10 2019 *)

CROSSREFS

Cf. A000312, A112354, A305787.

Sequence in context: A316085 A068691 A093135 * A202997 A093162 A328808

Adjacent sequences:  A305751 A305752 A305753 * A305755 A305756 A305757

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 10 2018

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 13 04:54 EDT 2020. Contains 336442 sequences. (Running on oeis4.)